Estimating causal quantile exposure response functions via matching

TL;DR

This paper introduces a new matching-based method for estimating causal quantile exposure-response functions with continuous treatments, combining propensity score matching and kernel quantile regression, validated through simulations and applied to environmental health data.

Contribution

It presents a novel two-step estimation procedure for causal quantile functions, including identification, asymptotic properties, and variance estimation, with practical application to pollution and health outcomes.

Findings

The method accurately estimates causal quantile effects in simulations.

It effectively adjusts for confounding in observational data.

Application to Medicare data reveals the impact of PM2.5 on hospital stay length.

Abstract

We develop new matching estimators for estimating causal quantile exposure-response functions and quantile exposure effects with continuous treatments. We provide identification results for the parameters of interest and establish the asymptotic properties of the derived estimators. We introduce a two-step estimation procedure. In the first step, we construct a matched data set via generalized propensity score matching, adjusting for measured confounding. In the second step, we fit a kernel quantile regression to the matched set. We also derive a consistent estimator of the variance of the matching estimators. Using simulation studies, we compare the introduced approach with existing alternatives in various settings. We apply the proposed method to Medicare claims data for the period 2012-2014, and we estimate the causal effect of exposure to PM$_{2.5}$ on the length of hospital stay for each zip code of the contiguous United States.